Method of forming a model representative of the distribution of a physical quantity in an underground zone, free of the effect of correlated noises contained in exploration data

Abstract

The invention is a method of estimating, from data obtained by exploration of a zone of a heterogeneous medium, a model representative of a distribution, in the zone, of at least one physical quantity, the model being free of a presence of correlated noises that may be contained in the data which has application to determining the distribution in an underground zone of acoustic impedance, propagation velocities and permeabilities, etc. The method includes acquiring measurements giving information about physical characteristics of the zone; specifying a noise modelling operator which associates, with a model of each physical quantity, synthetic data that constitute a response of the model; selecting a noise modelling operator which associates a correlated noise with a noise-generating function belonging to a predetermined space of the noise-generating functions; specifying a norm or of a semi-norm in the data space; specifying a semi-norm in the space of the noise-generating functions; defining a cost function; and adjusting the model and of the noise-generating functions.

Description

BACKGROUND OF THE INVENTION[0001]1. Field of the Invention[0002]The present invention relates to a method of forming, from data obtained by exploration of a zone of a heterogeneous medium, a model representative of the distribution in the zone of a physical quantity (at least partly) free of the presence of correlated noises that may be contained in the data.[0003]The method applies, for example, to the quantification of the acoustic impedance in an underground zone.[0004]2. Description of the Prior Art[0005]The process of seeking a model that adjusts to experimental measurements has been developed in nearly all the fields of the sciences or technology. Such an approach is known under various names: least-squares method for parameters estimation, for inverse problem solution. For a good presentation of this approach within the context of geosciences, one may for example refer to:[0006]Tarantola, A.: “Inverse Problem Theory: Method for Data Fitting and Model Parameter Estimation”, El...

AI Technical Summary

Benefits of technology

[0024]g) adjustment of the model and of the noise-generating functions by minimizing the cost function, by means of an algorithmic method taking advantage of the isometry properties of the noise modelling operators.

Problems solved by technology

The measuring results often contain errors.

Modelling noises add further to these measuring errors when the experimentation is compared with modelling results: modellings are never perfect and therefore always correspond to a simplified view of reality.

When the data contain correlated noises, the quality of the model estimated by solving the inverse problem can be seriously affected thereby.

As already mentioned, no modelling operator is perfect.

Among these people, seismic exploration practitioners are among the most concerned ones: in fact, their data have a poor or even very bad signal-to-noise ratio.

However, these techniques are not perfect: they presuppose that a transformation allowing complete separation of the signal and of the noise has been found.

In this context, correlated noises are particularly bothersome because they can be difficult to separate from the signal (which is also correlated) and can have high amplitudes.

It is therefore often difficult to manage the following compromise: either the signal is preserved, but a large noise residue remains, or the noise is eliminated, but then the signal is distorted.

However, according to the authors, an increase by an order of magnitude of the computing time required for solution of the conventional inverse problem, that is without seeking the correlated component of the noise, is the price to pay for these performances.

Furthermore, the result obtained with the method is extremely sensitive to any inaccuracy introduced upon definition of operator T: this is the ineluctable compensation for the high aptitude of the method to discriminate signal and noise.

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